# User:Patrick/wt

This page aims to list articles on Wikipedia that are related to Talk:Astronomy, Talk:Astrophysics and Talk:Cosmology. This is so that those interested in the subject can monitor changes to the pages by clicking on Related changes in the sidebar.

The list is not necessarily complete or up to date - if you see an article that should be here but isn't (or one that shouldn't be here but is), please do update the page accordingly.

Three astronomy related WikiProjects are being developed, please visit [[Talk:Wikipedia:WikiProject Astronomical Objects|WikiProject Astronomical Objects]], [[Talk:Wikipedia:WikiProject Constellations|WikiProject Constellations]], and [[Talk:Wikipedia:WikiProject Telescopes|WikiProject Telescopes]].

This is a list of Talk:geography topics:

## Miscellaneous

Gravitation is the tendency of Talk:masses to move toward each other.

The first mathematical formulation of the theory of gravitation was made by Talk:Sir Isaac Newton and proved astonishingly accurate. He postulated the force of "universal gravitational attraction".

Newton's theory has now been replaced by Talk:Albert Einstein's theory of Talk:General relativity but for most purposes dealing with weak gravitational fields (for example, sending rockets to the moon or around the solar system) Newton's formulae are sufficiently accurate. For this reason Newton's law is often used and will be presented first.

## Newton's law of universal gravitation

[[Talk:Image:Gravityroom.png|thumb|222px|Gravity in a room: the curvature of the Earth is negligible at this scale, and the force lines can be considered being parallel]]

Newton's Talk:law of universal gravitation states the following:

Every object in the Talk:Universe attracts every other object with a Talk:force directed along the line of centers for the two objects that is Talk:proportional to the product of their masses and inversely proportional to the square of the separation between the two objects.

Considering only the magnitude of the force, and momentarily putting aside its direction, the law can be stated symbolically as follows.

${\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}}$

where

• F is the maganitude of the gravitational force between two objects
• m1 is the mass of first object
• m2 is the mass of second object
• r is the distance between the objects
• G is the Talk:gravitational constant, that is approximately : G = 6.67 × 10−11 N m2 kg-2

Strictly speaking, this law applies only to point-like objects. If the objects have spatial extent, the force has to be calculated by integrating the force (in vector form, see below) over the extents of the two bodies. It can be shown that for an object with a spherically-symmetric distribution of mass, the integral gives the same gravitational attraction on masses outside it as if the object were a point mass.

This law of universal gravitation was originally formulated by Talk:Isaac Newton in his work, the Principia Mathematica (Talk:1687). The history of the gravitation as a physical concept is considered in more detail below.

### Vector form

[[Talk:Image:Gravitymacroscopic.png|thumb|200px|Gravity on a macroscopic scale]]

Newton's law of universal gravitation can be written as a vector Talk:equation to account for the direction of the gravitational force as well as its magnitude. In this formulation, quantities in bold represent vectors.

${\displaystyle \mathbf {F} _{12}=G{m_{1}m_{2} \over r_{21}^{2}}\,\mathbf {\hat {r}} _{21}}$

As before, m1 and m2 are the masses of the objects 1 and 2, and G is the gravitational constant.

It can be seen that the vector form of the equation is the same as the Talk:scalar form, except for the vector value of F and the unit vector. Also, it can be seen that F12 = − F21.

Gravitational acceleration is given by the same formula except for one of the factors m:

${\displaystyle \mathbf {a} =G{m \over r^{2}}\,\mathbf {\hat {r}} }$

## Einstein's theory of gravity

Newton's formulation of gravity is quite accurate for most practical purposes. There are a few problems with it though:

1. It assumes that gravitational force is transmitted instantaneously by a posited method, "action at a distance". However, even Newton felt action at a distance to be [[Talk:#Newton's reservations|unsatisfactory]].
2. Newton's Talk:model of absolute space and time was eventually contradicted by Einstein's theory of Talk:special relativity in the Talk:twentieth century. Einstein's theory of special relativity was successfully built on the backbone of the experimentally supported assumption that there exists some velocity at which signals can be transmitted, the Talk:speed of light in vacuum.
3. It does not explain the Talk:precession of the Talk:perihelion of the Talk:orbit of the Talk:planet Mercury. This precession is small; the unexplained portion is on the order of one angular second per century (an arc-second per century).
4. It predicts that light is deflected by gravity. However, this predicted deflection is only half as much as observations of this deflection, which were made after General Relativity was developed in Talk:1915.
5. The observed fact that gravitation and inertial mass are the same (or at least proportional) for all bodies is unexplained within Newton's system. See Talk:equivalence principle.

Talk:Einstein developed a new theory called Talk:general relativity which includes a theory of gravity, published in Talk:1915. The gravitational aspect of this theory says that the presence of matter "warps" Talk:spacetime. Objects in Talk:free fall in the universe take Talk:geodesics in spacetime. A geodesic is the counterpart of a straight line in Euclidean geometry.

### How spacetime curvature simulate gravitational force

The curvature of spacetime considered as a whole implies a rather complex picture that is usually treated with the tools of Talk:differential geometry and that requires the use of Talk:tensor calculus. It is possible though to understand - at least approximately - the mechanism of gravitation without tensors when the total curvature of spacetime is split into two components:

Both components of curvature are responsible for gravity according to Einstein's theory.

The effect of the first component, the curvature of space, is negligible in all cases when the velocities of objects are much smaller than speed of light and when the ratios of masses divided by the distances separating them are much smaller than a specific constant, namely the ratio of speed of light squared to Newtonian gravitational constant: ${\displaystyle c^{2}/G\approx 10^{27}kg/m}$. So for the majority of cases in the universe, and certainly for almost all cases in our solar system except precession of perihelion of Mercury and deflection of light rays in the vicinity of sun, we may treat the space as flat, as ordinary Euclidean space. It leaves us only with the gravitational time dilation as a possible reason for the illusion of "gravitational force" acting at the distance. Assuming that the masses are smaller than the distances divided by the constant above, the time dilation is tiny, but it is enough to cause Newtonian gravity as we know it.

The reason for this illusion is this: any mass in the universe modifies the rate of time in its vicinity this way that time runs slower closer to the mass and the change of time rate is controlled by an equation having exactly the same form as the equation that Newton discovered as his "Law of Universal Gravitation". The difference between them is in essence not in form since the Newtonian potential is replaced by the Einsteinian time rate ${\displaystyle d\tau /dt}$, where ${\displaystyle \tau }$ is the time at a point at vicinity of the mass (the proper time of objects at this point in space, the time that is measured by the clocks in this point) and ${\displaystyle t}$ is the time at observer at infinity, with the right side of the equation ${\displaystyle 1-GM/(c^{2}r)\,\!}$ staying the same as in Newtonian equation (with accuracy to irrelevant constants). Because of the same form of both equations, the path of the object that takes an extremum of proper time while traveling, and by this taking a geodesic in spacetime, is the same (with accuracy to the negligible in this case curvature of space) as the Newtonian orbit of this object around the mass. So it looks as if the path of the object were bent by some "force of attraction" between the object and the mass. Since bending of the object's path is clearly visible and the time dilation extremely difficult to notice, a (fictitious) "gravitational force" has been assumed rather than a (real, presently measured with precise enough and formerly unavailable clocks) time dilation as the reason for bending paths of objects moving in vicinity of masses.

So without any force involved into keeping the traveling object in line the object follows the Newtonian orbit in space just by following a geodesic in spacetime. This is Einstein's explanation why without any "gravitational forces" all the objects follow Newtonian orbits and at the same time why the Newtonian gravitation is the approximation of the Einsteinian gravitation.

In this way the Newton's "Law of Universal Gravitation" that looked to people who tried to interpret it as an equation describing a hypothetical "force of gravitational attraction" acting at a distance (except to Newton himself who didn't believe that "action at a distance" is possible) turned out to be really an equation describing spacetime geodesics in Euclidean space. We may say that Newton discovered the geodesic motion in spacetime and Einstein, by applying Riemannian geometry to it, extended it to curved spacetime, disclosed the hidden Newtonian physics, and made its math accurate.

### How energy is conserved if no forces act at a distance

It often puzzles students of Einstein's gravity that without any force acting at distance the kinetic energy of a free falling objects changes. The puzzling question is "where is this kinetic energy coming from, when the object is moving down; or going to, when the object is moving up"? The old "gravitational field" of the "attractive force" that was considered to be a repository of this "gravitational energy" in Newton's gravity isn't any good any more since now, if "attractive force" is zero, so is the "gravitational field". We need to identify another repository for this energy.

As we know the total energy of an object is ${\displaystyle E=mc^{2}\,\!}$, where ${\displaystyle m}$ is the so-called "Talk:relativistic mass", and ${\displaystyle c}$ is the speed of light. When an object falls "down" its kinetic energy goes up. Energy has mass and so ${\displaystyle m}$ goes up. However ${\displaystyle c^{2}}$ drops down by the same amount since the falling object gets into space where time is running slower (recall time dilation) and so the speed of light, as observed by the same distant observer who is seeing the increasing kinetic energy, is slower as well (that's why the speed of light is not constant in a gravitational field). If both ${\displaystyle m}$ and ${\displaystyle c^{2}}$ change in opposite directions by the same amount, the product (the total energy of the object) stays the same for a free falling object. That's how the conservation of energy works in Einstein's gravity.

There is one important result of Einstein's gravity: to keep the change of ${\displaystyle c^{2}}$ the same as change of ${\displaystyle m}$ there must be a relative increase in amount of space (space curvature) equal to the relative time dilation. It might be said that nature has to curve space by the same amount as time gets dilated because of nature's inability to create energy from nothing.

### Why Einstein's gravity differs from Newton's

Einsteinian gravitation is not just a small modification of Newtonian gravity. Even in the limit in which general relativity can be well approximated by Newton's equations, the Talk:gravitational potential of the Newtonian theory only knows about the time dilation portion of the Einsteinian gravitational field. The space curvature is not found in the Newtonian framework at all. In all cases when the space curvature becomes relevant - like in close enough proximity to big enough masses, like stars or in the context of large enough velocities - the curvature of space can't be neglected and the predictions of Newtonian and Einsteinian theories start to differ markedly. Every time such a difference was measured, the Einsteinian theory was much closer to the actual observations - essentially, its predictions were always exact.

In particular the Einsteinian gravitation explained why Talk:Mercury's precession differs from Newtonian prediction: since Mercury is the closest planet to the sun it moves faster than any other planet, and also it is in more curved space than all other planets. This is reflected in the behavior of Mercury and the Einsteinian calculations predict this behavior within observational error.

The other Einsteinian prediction is bending light rays in vicinity of the sun. Since the Newtonian deflection of the ray corresponds only to the time dilation, and since it happens for the reasons explained in the previous section that the relative curvature of space must be the same as the relative time dilation, the total deflection is twice as big as its Newtonian prediction. The Einsteinian prediction being twice as big as Newtonian is again within the observational error.

Yet despite such an "elegant" simplification of physics (and simpler in physics is more elegant) as Einsteinian elimination of action at a distance, only the observational differences between theories count in science since it is very easy to be mislead by "elegance of logic". As Einstein said "the elegance should concern a tailor rather than a physicist". He also said that "things should be made as simple as possible but not any simpler".

E.g. before Talk:1998 a group of prominent gravity physicists maintained that to make Talk:Einstein's field equation even simpler requires to remove Einstein's Talk:cosmological constant from it. They advertised this constant as an "Einstein's biggest blunder" (apparently a term coined by Einstein himself). Lack of this constant in Einstein's field equation predicted a decelerating Talk:expansion of space, which in turn was strongly advocated by almost all gravity physicists at that time. It was called Talk:standard model of cosmology. Proving that the expansion is decelerating due to "tremendous gravitational attraction of all masses of the universe" (in Einsteinian theory where there is no "gravitational attraction" at all) was supposed to be the first proof ever that cosmology is science after all, since finally it would be able to predict something. A team of enthusiastic young astronomers has been appointed to confirm this prediction. In Talk:1998 the results came in. It turned out that the prediction is false: the space of our universe looks as if it were expanding at accelerating rate.

## Units of measurement and variations in gravity

Gravitational phenomena are measured in various units, depending on the purpose. The Talk:gravitational constant is measured in newtons times Talk:metre squared per Talk:kilogram squared. Gravitational acceleration, and acceleration in general, is measured in Talk:metre per second squared or in galileos or gees. The acceleration due to gravity at the Earth's surface is approximately 9.81 m/s2, depending on the location. A standard value of the Earth's gravitational acceleration has been adopted, called g. When the typical range of interesting values is from zero to several thousand galileos, as in aircraft, acceleration is often stated in multiples of g. When used as a measurement unit, the standard acceleration is often called "gee", as g can be mistaken for g, the Talk:gram symbol. For other purposes, measurements in multiples of milligalileo (1/1000 galileo) are typical, as in Talk:geophysics. A related unit is the eotvos, which is the unit of the gravitational Talk:gradient. Mountains and other geological features cause subtle variations in the Earth's gravitional field; the magnitude of the variation per unit distance is measured in eotvos.

Typical variations with time are 0.2 mgal during a day, due to the Talk:tides, i.e. the gravity due to the moon and the sun.

## Gravity, and the acceleration of objects near the Earth

The acceleration due to the apparent "force of gravity" that "attracts" objects to the surface of the earth is not quite the same as the acceleration that is measured for a free-falling body at the surface of the earth (in a frame at rest on the surface). This is because of the rotation of the earth, which leads (except at the poles) to a centrifugal force which slightly lessens the acceleration observed. See Talk:Coriolis effect.

## Comparison with electromagnetic force

The gravitational interaction of Talk:protons is approximately a factor 1036 weaker than the electromagnetic repulsion. This factor is independent of distance, because both interactions are inversely proportional to the square of the distance. Therefore on an atomic scale mutual gravity is negligible. However, the main interaction between common objects and the earth and between celestial bodies is gravity, because gravity is electrically neutral: even if in both bodies there were a surplus or deficit of only one Talk:electron for every 1018 protons and Talk:neutrons this would already be enough to cancel gravity (or in the case of a surplus in one and a deficit in the other: double the interaction).

In terms of Talk:Planck units: the charge of a proton is 0.085, while the mass is only 8 × 10-20. From that point of view, the gravitational force is not small as such, but because masses are small.

The relative weakness of gravity can be demonstrated with a small Talk:magnet picking up pieces of Talk:iron. The small magnet is able to overwhelm the gravitational interaction of the entire earth.

Gravity is small unless at least one of the two bodies is large or one body is very dense and the other is close by, but the small gravitational interaction exerted by bodies of ordinary size can fairly easily be detected through experiments such as the Cavendish torsion bar experiment.

[[Talk:Image:M13grav.jpg|thumb|Talk:Globular Cluster M13 demonstrates gravitational field.]]

## Gravity and quantum mechanics

It is strongly believed that three of the four Talk:fundamental forces (the Talk:strong nuclear force, the Talk:weak nuclear force, and the Talk:electromagnetic force) are manifestations of a single, more fundamental force. Combining gravity with these forces of Talk:quantum mechanics to create a theory of Talk:quantum gravity is currently an important topic of research amongst physicists. General relativity is essentially a geometric theory of gravity. Quantum mechanics relies on interactions between particles, but general relativity requires no particles in its explanation of gravity. Scientists have theorized about the Talk:graviton (a particle that transmits the force gravity) for years, but have been frustrated in their attempts to find a consistent Talk:quantum theory for it. Many believe that Talk:string theory holds a great deal of promise to unify general relativity and Talk:quantum mechanics, but this promise has yet to be realized. It never can be for obvious reasons if Einstein's theory is true, due to the non-existence of "gravitational attraction" (explained in the above section "Einstein's Theory of Gravity")

## Experimental tests of theories

Today General Relativity is accepted as the standard description of gravitational phenomena. (Alternative theories of gravitation exist but are more complicated than General Relativity.) General Relativity is consistent with all currently available measurements of large-scale phenomena. For weak gravitational fields and bodies moving at slow speeds at small distances, Einstein's General Relativity gives almost exactly the same predictions as Newton's law of gravitation.

Crucial experiments that justified the adoption of General Relativity over Newtonian gravity were the classical tests: the Talk:gravitational redshift, the deflection of light rays by the Sun, and the Talk:precession of the orbit of Mercury.

General relativity also explains the equivalence of gravitational and inertial mass, which has to be assumed in Newtonian theory.

More recent experimental confirmations of General Relativity were the (indirect) deduction of gravitational waves being emitted from orbiting Talk:binary stars, the existence of Talk:neutron stars and black holes, Talk:gravitational lensing, and the convergence of measurements in observational Talk:cosmology to an approximately flat model of the observable Talk:Universe, with a matter density parameter of approximately 30% of the Talk:critical density and a Talk:cosmological constant of approximately 70% of the critical density.

Even to this day, scientists try to challenge General Relativity with more and more precise direct experiments. The goal of these tests is to shed light on the yet unknown relationship between Gravity and Quantum Mechanics. Space probes are used to either make very sensitive measurements over large distances, or to bring the instruments into an environment that is much more controlled than it could be on Earth. For example, in Talk:2004 a dedicated Talk:satellite for gravity experiments, called Talk:Gravity Probe B, was launched. Also, land-based experiments like Talk:LIGO are gearing up to possibly detect gravitational waves directly.

Talk:Speed of gravity: Einstein's theory of relativity predicts that the speed of gravity (defined as the speed at which changes in location of a mass are propagated to other masses) should be consistent with the speed of light. In 2002, the Fomalont-Kopeikin experiment produced measurements of the speed of gravity which matched this prediction. However, this experiment has not yet been widely peer-reviewed, and is facing criticism from those who claim that Fomalont-Kopeikin did nothing more than measure the speed of light in a convoluted manner.

## History

Although the law of universal gravitation was first clearly and rigorously formulated by Isaac Newton, the phenomenon was more or less seen by others. Even Talk:Ptolemy had a vague conception of a force tending toward the center of the earth which not only kept bodies upon its surface, but in some way upheld the order of the universe. Talk:Johannes Kepler inferred that the planets move in their orbits under some influence or force exerted by the sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to make a precise statement of the nature of the force. Talk:Christiaan Huygens and Talk:Robert Hooke, contemporaries of Newton, saw that Kepler's third law implied a force which varied inversely as the square of the distance. Newton's conceptual advance was to understand that the same force that causes a thrown rock to fall back to the Earth keeps the planets in Talk:orbit around the Sun, and the Moon in orbit around the Earth.

Newton was not alone in making significant contributions to the understanding of gravity. Before Newton, Talk:Galileo Galilei corrected a common misconception, started by Talk:Aristotle, that objects with different mass fall at different rates. To Aristotle, it simply made sense that objects of different mass would fall at different rates, and that was enough for him. Galileo, however, actually tried dropping objects of different mass at the same time. Aside from differences due to friction from the air, Galileo observed that all masses accelerate the same. Using Newton's equation, ${\displaystyle F=ma}$, it is plain to us why:

${\displaystyle F=-{Gm_{1}m_{2} \over r^{2}}=m_{1}a_{1}}$

The above equation says that mass ${\displaystyle m_{1}}$ will accelerate at Talk:acceleration ${\displaystyle a_{1}}$ under the force of gravity, but divide both sides of the equation by ${\displaystyle m_{1}}$ and:

${\displaystyle a_{1}={Gm_{2} \over r^{2}}}$

Nowhere in the above equation does the mass of the falling body appear. When dealing with objects near the surface of a planet, the change in r divided by the initial r is so small that the acceleration due to gravity appears to be perfectly constant. The acceleration due to gravity on Talk:Earth is usually called g, and its value is about 9.8 m/s2 (or 32 ft/s2). Galileo didn't have Newton's equations, though, so his insight into gravity's proportionality to mass was invaluable, and possibly even affected Newton's formulation on how gravity works.

However, across a large body, variations in ${\displaystyle r}$ can create a significant Talk:tidal force.

## Newton's reservations

It's important to understand that while Newton was able to formulate his law of gravity in his monumental work, he was not comfortable with it because he was deeply uncomfortable with the notion of "action at a distance" which his equations implied. He never, in his words, "assigned the cause of this power." In all other cases, he used the phenomenon of motion to explain the origin of various forces acting on bodies, but in the case of gravity, he was unable to experimentally identify the motion that produces the force of gravity. Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science.

He lamented the fact that 'philosophers have hitherto attempted the search of nature in vain' for the source of the gravitational force, as he was convinced 'by many reasons' that there were 'causes hitherto unknown' that were fundamental to all the 'phenomena of nature.' These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer is yet to be found. While it is true that Einstein's hypotheses are successful in explaining the effects of gravitational forces more precisely than Newton's in certain cases, he too never assigned the cause of this power, in his theories. It is said that in Einstein's equations, 'matter tells space how to curve, and space tells matter how to move,' but this new idea, completely foreign to the world of Newton, does not enable Einstein to assign the 'cause of this power' to curve space any more than the Law of Universal Gravitation enabled Newton to assign its cause. In Newton's own words:

I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain.

If science is eventually able to discover the cause of the gravitational force, Newton's wish could eventually be fulfilled as well.

It should be noted that here, the word "cause" is not being used in the same sense as "cause and effect" or "the defendant caused the victim to die." Rather, when Newton uses the word "cause," he (apparently) is referring to an "explanation." In other words, a phrase like "Newtonian gravity is the cause of planetary motion" means simply that Newtonian gravity explains the motion of the planets. See Talk:Causality and Talk:Causality (physics).

## Self-gravitating system

A self-gravitating system is a system of masses kept together by mutual gravity. An example is a Talk:binary star.

## Special applications of gravity

A height difference can provide a useful pressure in a liquid, as in the case of an Talk:intravenous drip and a water Talk:tower.

A weight hanging from a cable over a Talk:pulley provides a constant tension in the cable, also in the part on the other side of the pulley.

## Comparative gravities of different planets

The acceleration due to gravity at the Earth's surface is, by convention, equal to 9.80665 metres per second squared. (The actual value varies slightly over the surface of the Earth; see Talk:gee for details.) This quantity is known variously as gn, ge, g0, gee, or simply g. The following is a list of the gravitational accelerations (in multiples of g) at the surfaces of each of the planets in the solar system:

 Mercury 0.376 Venus 0.903 Earth 1 Mars 0.38 Jupiter 2.34 Saturn 1.16 Uranus 1.15 Neptune 1.19 Pluto 0.066

Note: The "surface" is taken to mean the cloud tops of the gas giants (Jupiter, Saturn, Uranus and Neptune) in the above table.

For spherical bodies surface gravity in m/s2 is 2.8 × 10−10 times the radius in m times the average density in kg/m3.

Mathematical models are of great importance in Talk:physics. Physical theories are almost invariably expressed using Talk:mathematical models, and the mathematics involved is generally more complicated than in the other sciences. Different mathematical models use different geometries that are not necessarily entierly accurate descriptions of the geometry of the universe. Talk:Euclidean geometry is much used in classical physics, while Talk:general relativity is one of the theories that use Talk:non-Euclidean geometry.

An example of how geometry does not accurately represent the universe comes in the Talk:Banach-Tarski paradox which have consqequences such as that a marble can be cut up into finitely many pieces and reassembled into a planet, or a telephone could be cut up and reassembled as a water lily. These transformations are not possible with real objects made of atoms, but it is possible with their geometric shapes.

It is common to use idealized models in physics to simplify things. Massless ropes, point particles, Talk:ideal gas and Talk:particle in a box are among the many simplified models used in physics.

Throughout history, more and more accurate mathematical models have been developed. Talk:Newton's laws accurately describe many everyday fenomena, but at certain limits Talk:relativity theory and Talk:quantum mechanics must be used, even these do not apply to all situations and need further refinement. It is possible to obtain the less accurate models in approproate limits, for example relativistic mechanics reduce to Newtonian mechanics when the speed much less than the Talk:speed of light. Quantum mechanics reduce to classical physics when the quantum numbers are high. If we say that a tennisball is a particle and calculate its Talk:de Broglie wavelength is will turn out to be insignificantly small so it is seen that classical physics is better to use than quantum mechanics in this case.

The laws of physics are represented with simple equations such as Newton's laws, Maxwells equation and the Schrödinger equation. These laws are such as a basis for making mathematical models of real situations. Many real situations are very complex and thus modeled approximate on a computer, a model that is computationally feasible to compute is made from the basic laws or from approximate models made from the basic laws. For example molecules can be modeled by Talk:molecular orbital models that are approximate solutions to the Schrödinger equation. In Talk:engineering, physics models are often made by mathematical methods such as Talk:finite element analysis.

[[Talk:Image:minuteman3launch.jpg|framed|A Talk:Minuteman III missile soars after a test launch.]] An intercontinental ballistic missile, or ICBM, is a long-range Talk:ballistic missile using a ballistic Talk:trajectory involving a significant ascent and descent, including Talk:sub-orbital flight. The Talk:FOBS had a partial orbital trajectory. An ICBM differs little technically from other Talk:ballistic missiles such as Talk:intermediate-range ballistic missiles, short-range ballistic missiles, or the newly named theater ballistic missiles; these are differentiated only by maximum range. The maximum range of ICBMs is addressed by arms control agreements, which prohibit orbital or fractional-orbital weapons. Only three nations currently have operational ICBM systems: the Talk:United States, Talk:Russia, and China. However, other nations have ICBMs but not an organized ICBM system, such as Talk:Israel, Talk:India, Talk:Iran, Talk:North Korea, and Talk:Pakistan.

In Talk:2002, the United States and Russia agreed in the Talk:SORT treaty to reduce their deployed stockpiles to not more than 2,200 warheads each.

## Flight phases

The following flight phases can be distinguished:

## History

Early ICBMs formed the basis of many space launch systems. Examples include: Atlas, Delta, Talk:Redstone_rocket, Titan, R-7, and Proton. Modern ICBMs tend to be smaller than their ancestors (due to increased accuracy and smaller and lighter warheads) and use solid fuels, making them less useful as orbital launch vehicles.

Countries beginning developing ICBMs have all used liquid propellants initially, because the technology is easier.

## Modern ICBMs

Modern ICBMs typically carry Talk:multiple independently targetable reentry vehicles (MIRVs), each of which carries a separate nuclear warhead, allowing a single missile to hit multiple targets. MIRV was an outgrowth of the rapidly shrinking size and weight of modern warheads and the Strategic Arms Limitation Treaties which imposed limitations on the number of launch vehicles(Talk:SALT I and Talk:SALT II). It has also proved to be an "easy answer" to proposed deployments of ABM systems – it is far less expensive to add more warheads to an existing missile system than to build an ABM system capable of shooting down the additional warheads; hence, most ABM system proposals have been judged to be impractical. The only operational ABM systems were deployed in the 1970's, the US Safeguard ABM facility was located in North Dakota and was operational from 1975-1976. The USSR deployed its Galosh ABM system was deployed around Moscow in the 1970's and remains in service.

[[Talk:Image:Titan 1 complex.jpg|thumb|250px|right|The Talk:Titan I ICBM Underground Silo Complex includes a network of tunnels connecting multiple silos to subterranian control and communications facilities.]]

Modern ICBMs tend to use solid fuel, which can be stored easily for long periods of time. Liquid-fueled ICBMs were generally not kept fueled all the time, and therefore fueling the rocket was necessary before a launch. ICBMs are based either in Talk:missile silos, which offer some protection from military attack (including, the designers hope, some protection from a nuclear first strike), or on Talk:submarines, rail cars or heavy trucks, which are mobile and therefore hard to find.

The low flying, guided Talk:cruise missile is an alternative to Talk:ballistic missiles.

## Specific missiles

### Land-based intercontinental ballistic missiles (ICBMs) and cruise missiles

The US Air Force currently operates just over 500 Talk:ICBMs at around 15 missile complexes located primarily in the northern Rocky Mountain states and the Dakotas. These are of the Talk:Minuteman III and Peacekeeper ICBM variants. Peacekeeper missiles are being phased out by 2005. All USAF Talk:Minuteman II missiles have been destroyed in accordance to START, and their launch silos sealed or sold to the public. To comply with the Talk:START II most US multiple independently targetable reentry vehicles, or Talk:MIRV’s, have been eliminated and replaced with single warhead missiles. However, since the abandonment of the START II treaty, the U.S. is said to be considering retaining 800 warheads on 500 missiles.[1]

### Sea-based ICBMs

• The Talk:French Navy constantly maintains at least four active units, relying on two classes of Talk:SSBNs: the older Redoutable class, which are progressively decomissioned, and the newer Triomphant class. These carry 16 M45 missiles with TN75 warheads, and are sceduled to be upgraded to M51 nuclear missile around 2010.

### Current and former US ballistic missiles

• Atlas (SM-65, CGM-16) former ICBM launched from silo, now the rocket is used for other purposes
• Talk:Titan I (SM-68, HGM-25A)
• Talk:Titan II (SM-68B, LGM-25C) - former ICBM launched from silo, now the rocket is used for other purposes
• Minuteman I (SM-80, LGM-30A/B, HSM-80)
• Minuteman II (LGM-30F)
• Minuteman III (LGM-30G) - launched from silo - as of Talk:June 28, Talk:2004, there are 517 Minuteman III missiles in active inventory
• Talk:LG-118A Peacekeeper / MX (LG-118A, MX) - silo-based; 29 missiles were on alert at the beginning of 2004; all are to be removed from service by 2005.
• Midgetman - has never been operational - launched from mobile launcher
• Polaris - former SLBM
• Poseidon - former SLBM
• Trident - SLBM - Trident II (D5) was first deployed in 1990 and is planned to be deployed past 2020.

### Soviet/Russian

Specific types of Soviet/Russian ICBMs include:

## Ballistic missile submarines

Specific types of Talk:ballistic missile Talk:submarines include:

For information on how large numbers are named in English, see Talk:names of large numbers.

Large numbers are Talk:numbers that are large compared with the numbers used in everyday life. Very large numbers often occur in fields such as Talk:mathematics, Talk:cosmology and Talk:cryptography. Sometimes people refer to numbers as being "astronomically large". However, mathematically it is easy to define numbers that are much larger than occur even in astronomy.

## Writing and thinking about large numbers

Large numbers are often found in science, and Talk:scientific notation was created to handle both these large numbers and also very small numbers. 1.0 × 109, for example, means one billion, a 1 followed by nine zeros: 1,000,000,000, and 1.0 × 10-9 means one billionth, or 0.0000000001. Writing 109 instead of nine zeros saves the reader the effort and hazard of counting a long string of zeros to see how large the number is.

Adding a 0 to a large number multiplies it by ten: 100 is ten times 10. In scientific notation, however, the exponent only increases by one, from 101 to 102. Remember then, when reading numbers in scientific notation, that small changes in the exponent equate to large changes in the number itself: 2.5 × 105 dollars ($250,000) is a common price for new homes in the U.S., while 2.5 × 1010 dollars ($25 billion) would make you one of the world's richest people.

## Large numbers in the everyday world

Some large numbers apply to things in the everyday world.

Examples of large numbers describing everyday real-world objects are:

• cigarettes smoked in the Talk:United States in one year, on the order of 1012 (one trillion)
• bits on a computer hard disk (typically 1012 to 1013)
• number of cells in the human body > 1014
• number of neuron connections in the human brain, 1014 (estimated)
• Talk:Avogadro's number, approximately 6.022 × 1023

Other examples are given in Talk:Orders of magnitude (numbers).

## Large numbers and computers

Talk:Moore's Law, generally speaking, estimates that computers double in speed about every 18 months. This sometimes leads people to believe that eventually, computers will be able to solve any mathematical problem, no matter how complicated. This is not the case; computers are fundamentally limited by the constraints of physics, and certain upper bounds on what we can expect can be reasonably formulated.

First, a rule of thumb for converting between scientific notation and powers of two, since computer-related quantities are frequently stated in powers of two. Since the logarithm of 10 in base 2 is a little more than 3, multiplying a scientific notation exponent by 3 gives its approximate value as an exponent with a base of 2. For example, 103 (1000) is somewhere in the neighborhood of 29 (512). (But remember that when dealing with very large numbers, such "neighborhoods" will themselves be quite large).

Between 1980 and 2000, hard disk sizes increased from about 10 megabytes (1 × 107) to over 100 gigabytes (1 × 1011). A 100 gigabyte disk could store the names of all of Earth's six billion inhabitants without using data compression. But what about a dictionary-on-disk storing all possible passwords containing up to 40 characters? Assuming each character equals one byte, there are about 2320 such passwords, which is about 2 × 1096. This paper points out that if every particle in the universe could be used as part of a huge computer, it could store only about 1090 bits, less than one millionth of the size our dictionary would require.

Of course, even if computers can't store all possible 40 character strings, they can easily programmed to start creating and displaying them one at a time. As long as we don't try to store all the output, our program could run indefinitely. Assuming a modern PC could output 1 billion strings per second, it would take one billionth of 2 × 1096 seconds, or 2 × 1087 seconds to complete its task, which is about 6 × 1079 years. By contrast, the universe is estimated to be 13.7 billion (1.37 × 1010) years old. Of course, computers will presumably continue to get faster, but the same paper mentioned before estimates that the entire universe functioning as a giant computer could have performed no more than 10120 operations since the Talk:big bang. This is trillions of times more computation than is required for our string-displaying problem, but simply by raising the stakes to printing all 50 character strings instead of all 40 character strings we can outstrip the estimated computational potential of even the universe itself.

Problems like our simple string-displaying example grow exponentially in the number of computations they require, and are one reason why exponentially difficult problems are called "intractible" in computer science: for even small numbers like the 40 or 50 characters we used in our example, the number of computations required exceeds even theoretical limits on mankind's computing power. The traditional division between "easy" and "hard" problems is thus drawn between programs that do and do not require exponentially increasing resources to execute.

Such limits work to our advantage in Talk:cryptography, since we can safely assume that any Talk:cipher-breaking technique which requires more than, say, the 10120 operations mentioned before will never be feasible. Of course, many ciphers have been broken by finding efficient techniques which require only modest amounts of computing power and exploit weaknesses unknown to the cipher's designer. Likewise, much of the research throughout all branches of computer science focuses on finding new, efficient solutions to problems that work with far fewer resources than are required by a naive solution. For example, one way of finding the Talk:greatest common divisor between two 1000 digit numbers is to compute all their factors by trial division. This will take up to 2 × 10500 division operations, far too large to contemplate. But the Talk:Euclidean algorithm, using a much more efficient technique, takes only a fraction of a second to compute the GCD for even huge numbers such as these.

As a general rule, then, PCs in 2004 can perform 240 calculations in a few minutes. A few thousand PCs working for a few years could solve a problem requiring 264 calculations, but no amount of traditional computing power will solve a problem requiring 2128 operations (which is about what would be required to break the 128-bit SSL commonly used in web browsers, assuming the underlying ciphers remain secure). Limits on computer storage are comparable. Talk:Quantum computers may allow certain problems to become feasible, but as of 2004 it is far too soon to tell.

## "Astronomically large" numbers

Other large numbers are found in Talk:astronomy:

Large numbers are found in fields such as Talk:mathematics and Talk:cryptography.

The Talk:MD5 Talk:hash function generates 128-bit results. There are thus 2128 (approximately 3.402×1038) possible MD5 hash values. If the MD5 function is a good hash function, the chance of a document having a particular hash value is 2-128, a value that can be regarded as equivalent to zero for most practical purposes. (But see Talk:birthday paradox.)

However, this is still a small number compared with the estimated number of Talk:atoms in the Talk:Earth, still less compared with the estimated number of atoms in the Talk:observable universe.

## Even larger numbers

Talk:Combinatorial processes rapidly generate even larger numbers. The Talk:factorial function, which defines the number of Talk:permutations of a set of unique objects, grows very rapidly with the number of objects.

Combinatorial processes generate very large numbers in Talk:statistical mechanics. These numbers are so large that they are typically only referred to using their Talk:logarithms.

Talk:Gödel numbers, and similar numbers used to represent bit-strings in Talk:algorithmic information theory are very large, even for mathematical statements of reasonable length. However, some pathological numbers are even larger than the Gödel numbers of typical mathematical propositions.

Examples:

The total amount of printed material in the world is 1.6 × 1018 bits, therefore the contents can be represented by a number which is ca. ${\displaystyle 2^{1.6\times 10^{18}}\approx 10^{4.8\times 10^{17}}}$

For a "power tower", the most relevant for the value are the height and the last few values. Compare with googolplex:

Also compare:

The first number is much larger than the second, due to the larger height of the power tower, and in spite of the small numbers 1.1 (however, if these numbers are made 1 or less, that greatly changes the result). Comparing the last number with ${\displaystyle 10^{\,\!10^{10}}}$, in the number 3000.48, the 1000 originates from the third number 1000 in the original power tower, a factor 3 comes from the second number 1000, and the minor term 0.48 comes from the first number 1000.

A very large number written with just three digits and ordinary exponentiation is ${\displaystyle 9^{\,\!9^{9}}\approx 10^{369,693,100}}$.

## Standardized system of writing very large numbers

A standardized way of writing very large numbers allows them to be easily sorted in increasing order, and one can get a good idea of how much larger a number is than another one.

Talk:Tetration with base 10 can be used for very round numbers, each representing an Talk:order of magnitude in a generalized sense.

Numbers in between can be expressed with a power tower of numbers 10, with at the top a regular number, possibly in scientific notation, e.g. ${\displaystyle 10^{\,\!10^{10^{10^{10^{4.829*10^{183230}}}}}}}$, a number between ${\displaystyle 10\uparrow \uparrow 7}$ and ${\displaystyle 10\uparrow \uparrow 8}$ (if the exponent quite at the top is between 10 and ${\displaystyle 10^{10}}$, like here, the number like the 7 here is the height).

If the height is too large to write out the whole power tower, a notation like ${\displaystyle (10\uparrow )^{183}(3.12*10^{6})}$ can be used, where ${\displaystyle (10\uparrow )^{183}}$ denotes a Talk:functional power of the function ${\displaystyle f(n)=10^{n}}$ (the function also expressed by the suffix "-plex" as in Talk:googolplex, see the Googol family).

Various names are used for this representation:

• base-10 exponentiated tower form
• tetrated-scientific notation
• incomplete (power) tower

The notation ${\displaystyle (10\uparrow )^{183}(3.12*10^{6})}$ is in ASCII ((10^)^183)3.12e6; a proposed simplification is 10^^183@3.12e6; the notations 10^^1@3.12e6 and 10^^0@3.12e6 are not needed, one can just write 10^3.12e6 and 3.12e6.

Thus googolplex = 10^^2@100 = 10^^3@2 = 10^^4@0.301; which notation is chosen may be considered on a number-by-number basis, or uniformly. In the latter case comparing numbers is sometimes a little easier. For example, comparing 10^^2@23.8 with 10^6e23 requires the small computation 10^.8=6.3 to see that the first number is larger.

To standardize the range of the upper value (after the @), one can choose one of the ranges 0-1, 1-10, or 10-1e10:

• In the case of the range 0-1, an even shorter notation is (here for googolplex) like 10^^3.301 (proposed by William Elliot). This is not only a notation, it provides at the same time a generalisation of 10^^x to real x>-2 (10^^4@0=10^^3, hence the integer before the point is one less than in the previous notation). This function may or may not be suitable depending on required smoothness and other properties; it is monotonically increasing and continuous, and satisfies 10^^(x+1) = 10^(10^^x), but it is only piecewise differentiable. The Talk:inverse function is a super-logarithm or hyper-logarithm, defined for all real numbers, also negative numbers. See also Extension of tetration to real numbers.
• The range 10-1e10 brings the notation closer to ordinary scientific notation, and the notation reduces to it if the number is itself in that range (the part "10^^0@" can be dispensed with).

Another example:

${\displaystyle 2\uparrow \uparrow \uparrow 4={\begin{matrix}\underbrace {2_{}^{2^{{}^{.\,^{.\,^{.\,^{2}}}}}}} \\\qquad \quad \ \ \ 65,536{\mbox{ copies of }}2\end{matrix}}\approx (10\uparrow )^{65,531}(6.0\times 10^{19,728})}$ (between ${\displaystyle 10\uparrow \uparrow 65,533}$ and ${\displaystyle 10\uparrow \uparrow 65,534}$)

The "order of magnitude" of a number (on a larger scale than usually meant), can be characterized by the number of times (say n) one has to take the ${\displaystyle log_{10}}$ to get a number between 1 and 10. Then the number is between ${\displaystyle 10\uparrow \uparrow n}$ and ${\displaystyle 10\uparrow \uparrow (n+1)}$

An obvious property that is yet worth mentioning is:

${\displaystyle 10^{(10\uparrow )^{n}x}=(10\uparrow )^{n}10^{x}}$

I.e., if a number x is too large for a representation ${\displaystyle (10\uparrow )^{n}x}$ we can make the power tower one higher, replacing x by ${\displaystyle log_{10}x}$, or find x from the lower-tower representation of the ${\displaystyle log_{10}}$ of the whole number. If the power tower would contain one or more numbers different from 10, the two approaches would lead to different results, corresponding to the fact that extending the power tower with a 10 at the bottom is then not the same as extending it with a 10 at the top (but, of course, similar remarks apply if the whole power tower consists of copies of the same number, different from 10).

If the height of the tower is not exactly given then giving a value at the top does not make sense, and a notation like ${\displaystyle 10\uparrow \uparrow (7.21*10^{8})}$ can be used.

If the value after the double arrow is a very large number itself, the above can recursively be applied on that value.

Examples:

${\displaystyle 10\uparrow \uparrow 10^{\,\!10^{10^{3.81*10^{17}}}}}$ (between ${\displaystyle 10\uparrow \uparrow \uparrow 2}$ and ${\displaystyle 10\uparrow \uparrow \uparrow 3}$)
${\displaystyle 10\uparrow \uparrow 10\uparrow \uparrow (10\uparrow )^{497}(9.73*10^{32})}$ (between ${\displaystyle 10\uparrow \uparrow \uparrow 4}$ and ${\displaystyle 10\uparrow \uparrow \uparrow 5}$)

Some large numbers which one may try to express in such standard forms include:

External link: Notable Properties of Specific Numbers (last page of a series which treats the numbers in ascending order, hence the largest numbers in the series)

## Accuracy

Note that for a number ${\displaystyle 10^{p}}$, one unit change in p changes the result by a factor 10. In a number like ${\displaystyle 10^{\,\!6.2\times 10^{3}}}$, with the 6.2 the result of proper rounding, the true value of the exponent may be 50 less or 50 more. Hence the result may be a factor ${\displaystyle 10^{50}}$ too large or too small. This is seemingly an extremely poor accuracy, but for such a large number it may be considered fair. The idea that it is the relative error that counts (a large error in a large number may be relatively small and therefore acceptable), is taken a step further here: the number is so large that even a large relative error may be acceptable. Perhaps what counts is the relative error in the exponent.

## Approximate arithmetic for very large numbers

In this context approximately equal may for example mean that two numbers are both written ${\displaystyle 10^{\,\!10^{10^{10^{10^{4.829*10^{183230}}}}}}}$, with the true values instead of 4.829 being e.g. 4.8293 and 4.8288.

Hence:

## Uncomputably large numbers

The Talk:busy beaver function Σ is an example of a function which grows faster than any computable function. Its value for even relatively small input is huge. The values of Σ(n) for n = 1, 2, 3, 4 are 1, 4, 6, 13. Σ(5) is not known but is definitely ≥ 4098. Σ(6) is at least 1.29×10865.

## Infinite numbers

See main article Talk:cardinal number

Although all these numbers above are very large, they are all still Talk:finite. Some fields of mathematics define Talk:infinite and Talk:transfinite numbers.

Beyond all these, Talk:Georg Cantor's conception of the Talk:Absolute Infinite surely represents the absolute largest possible concept of "large number".

## Notations

Some notations for extremely large numbers:

These notations are essentially functions of integer variables, which increase very rapidly with those integers. Ever faster increasing functions can easily be constructed recursively by applying these functions with large integers as argument.

Note that a function with a vertical asymptote is not helpful in defining a very large number, although the function increases very rapidly: one has to define an argument very close to the asymptote, i.e. use a very small number, and constructing that is equivalent to constructing a very large number, e.g. the reciprocal.

Talk:Orders of magnitude
Related articles
List of orders of magnitude for Talk:mass
Decade of Mass Mass using Talk:SI prefixes Mass of Item Item
10-35 kg 7 eV/c² = 1.2 × 10-35 kg upper limit of the rest mass of an Talk:electron neutrino
10-34 kg
10-33 kg
10-32 kg
10-31 kg 510.99906(15) 1 keV/c² = 9.1093897(54) × 10-31 kg rest mass of an Talk:electron
10-30 kg
10-29 kg
10-28 kg 105.658389(34) MeV/c² = 1.8835327(11) × 10-28 kg rest mass of a Talk:muon
10-27 kg 1 Talk:yoctogram (yg) ≈ 1.6605402 yg 1 Talk:atomic mass unit (amu) or Dalton (Da) ≈ mass of a Talk:hydrogen Talk:atom
938 MeV/c² = 1.6726231 × 10-27 kg mass of a Talk:proton - a neutron is the same mass to 3 places (mass of neutron > mass of proton)
10-26 kg 10 yg ≈ 30 yg mass of a Talk:water Talk:molecule
6.941 amu Talk:atomic mass of Talk:lithium
47.867 amu atomic mass of Talk:titanium
10-25 kg 100 yg 107.8682 amu atomic mass of Talk:silver
[259] amu atomic mass of Talk:nobelium
10-24 kg 1 Talk:zeptogram (zg) 1.6605402 zg = 1 Talk:kilodalton (kDa)
10-23 kg 10 zg
10-22 kg 100 zg
10-21 kg 1 Talk:attogram (ag)
10-20 kg 10 ag 10 ag mass of a small virus
10-19 kg 100 ag
10-18 kg 1 Talk:femtogram (fg)
10-17 kg 10 fg 1.1 × 10-17 kg mass equivalence of one Talk:joule
4.6 × 10-17 kg increase in mass by heating 1 g of Talk:water by 1 °C
10-16 kg 100 fg 6.65×10-16 kg (665 fg) Talk:E. coli bacterium
10-15 kg 1 Talk:picogram (pg)
10-14 kg 10 pg
10-13 kg 100 pg
10-12 kg 1 Talk:nanogram (ng) 1 ng mass of a human cell
10-11 kg 10 ng 80 ng Lethal dose of Talk:Botulinum toxin, the deadliest substance known, is about 1 ng/kg, so an 80 ng dose would kill almost anybody.
10-10 kg 100 ng
10-9 kg 1 Talk:microgram (μg) 2 μg Uncertainty in the mass of the prototype Talk:kilogram
10-8 kg 10 μg 2.2 × 10-8 kg the Talk:Planck mass
4.6 × 10-8 kg increase in mass by heating 1 ton of Talk:water by 100 °C
10-7 kg 100 μg 100μg average dose of a "hit" of Talk:LSD
200 μg average lethal dose of Talk:ricin
10-6 kg 1 Talk:milligram (mg) ≈ 0.3–13 mg mass of a grain of Talk:sand
1–2 mg typical mass of a Talk:mosquito
10-5 kg 10 mg 10–30 mg Dose of Talk:DXM per labeling on most products
Caffeine in most non-coffee drinks is in the bottom half of this range.
10-4 kg 100 mg Caffeine in a cup of coffee is in this range.
0.2 g 1 metric Talk:carat
100–200 mg Maximum legal caffeine pill in Talk:United States
0.3 g average hallucinogenic dose for Talk:mescaline
10-3 kg 1 Talk:gram (g) 1 g 1 Talk:millilitre of Talk:water at 4°C
~2.3 g, ~7 g Talk:United States dime: ~2.3 g, quarter: ~7 g, other common coins intermediate
10-2 kg 10 g 10 g approximate lethal dose of Talk:caffeine for an adult
17 g approximate mass of a Talk:mouse
24 g amount of Talk:ethanol in one drink
28.35 g 1 Talk:ounce (Talk:avoirdupois) &asymp
10-1 kg 100 g 150 g average mass of an adult human Talk:kidney
≈ 454 g 1 Talk:pound (Talk:avoirdupois)
1 kg 1 kg 1 kg 1 Talk:litre of Talk:water at 4°C
2–6 kg, 3 typical a newborn Talk:baby
4.0 kg women's Talk:shotput
5–7 kg a typical housecat
5–9 kg a Talk:pizote
7.3 kg men's Talk:shotput
101 kg 10 kg 10–30 kg a CRT computer monitor
15–20 kg a medium-sized dog
102 kg 100 kg 100 kg Talk:quintal (mainly U.S. - other countries have different definitions)
250 kg approximate mass of a Talk:lion
700 kg approximate mass of a dairy Talk:cow
910 kg 1 short Talk:ton (U.S.)
103 kg 1 Talk:tonne (t)
(1 Talk:megagram (Mg))
1000 kg 1 Talk:cubic metre of liquid Talk:water at 4°C
1,016.047 kg 1 Talk:ton (British) / 1 long Talk:ton (U.S.)
0.8–1.6 t typical passenger Talk:automobiles
104 kg 10 t 11 t Talk:Hubble Space Telescope
12 t largest Talk:elephant on record
14 t bell of Talk:Big Ben
the large dinosaurs go here somewhere
105 kg 100 t 100 t on average mass of largest animal, the Talk:blue whale
187 t Talk:International Space Station
600 t Talk:Antonov An-225 (the world's heaviest aircraft) maximum take-off mass
106 kg 1000 t
(1 Talk:gigagram (Gg))
1.5 × 106 kg mass of each gate of the Talk:Thames Barrier
2.041 × 106 kg launch mass of the Talk:Space Shuttle
107 kg 1.1 × 107 kg estimated annual production of Talk:Darjeeling Talk:tea
2.6 × 107 kg = 26 000 t = 26 kt Talk:Titanic
9.97 × 107 kg heaviest train: Australia's BHP Iron Ore, 2001 record
108 kg 6.5 × 108 kg mass of largest ship, Talk:Knock Nevis, when fully loaded
109 kg 1 Talk:teragram (Tg) = 1 Mt about 6 × 109 kg = 6 Mt mass of Talk:Great Pyramid of Giza
1010 kg 6 × 1010 kg = 60 Mt mass of Talk:concrete in the Talk:Three Gorges Dam, the world's largest concrete structure
1011 kg at least 2 × 1011 kg = 200 Mt Total mass of the world's humans
2 × 1011 kg = 300 Mt Mass of water stored in Talk:London storage reservoirs
1–8 × 1011 kg Estimated total mass of Antarctic Talk:krill, Euphausia superba, thought to be the most plentiful creature on the planet
1012 kg 1 Talk:petagram (Pg) = 1 Gt 3.91 × 1012 kg = 3.91 Gt World Talk:oil production in Talk:2001
1013 kg
1014 kg 2–3 × 1014 kg Estimated mass of rock exploded in eruption of Talk:Mount Tambora Talk:volcano in Talk:1815
1015 kg 1 Talk:exagram (Eg) = 1 Tt
1016 kg
1017 kg 1.23 × 1017 kg = 123 Tt Mass of a typical Talk:asteroid
1018 kg 1 Talk:zettagram (Zg) = 1 Pt 5 × 1018 kg = 5 Pt Mass of Talk:Earth's atmosphere
1019 kg
1020 kg 8.7 × 1020 kg = 870 Pt Mass of Talk:1 Ceres
1021 kg 1 Talk:yottagram (Yg) = 1 Et 1.35×1021 kg Total mass of Talk:Earth's Talk:oceans
1.6×1021 kg = 1.6 Et Mass of Charon
2.3×1021 kg Total mass of the Talk:Asteroid Belt
1022 kg 1.2 × 1022 kg Mass of Pluto
7.349 × 1022 kg = 73.49 Et Mass of Talk:Moon
1023 kg 1.2×1023 kg Mass of Titan
1.5×1023 kg Mass of Triton
1.5×1023 kg Mass of Ganymede
3.2×1023 kg Mass of Mercury
6.4×1023 kg Mass of Mars
1024 kg 1 Zt 4.9 × 1024 kg Mass of Venus
6.0×1024 kg = 6.0 Zt Mass of Talk:Earth
1025 kg 8.7 × 1025 kg Mass of Uranus
1026 kg 1.0 × 1026 kg Mass of Neptune
5.7 × 1026 kg Mass of Saturn
1027 kg 1 Yt 1.9 × 1027 kg Mass of Jupiter
1028 kg
1029 kg
1030 kg 2 × 1030 kg Mass of the Talk:Sun = 2000 Yt
approx. 3 × 1030 kg Talk:Chandrasekhar limit
1031 kg 4 × 1031 kg Mass of Talk:Betelgeuse
1032 kg
1033 kg
1034 kg
1035 kg
1036 kg
1037 kg
1038 kg Typical mass of a Talk:globular cluster
1039 kg
1040 kg
1041 kg 3.6 × 1041 kg Visible mass of the Talk:Milky Way galaxy
1042 kg 2 × 1042 kg Total mass of the Talk:Milky Way galaxy
1052 kg 2×1052 kg Mass of a Talk:critical density Talk:Universe
3 × 1052 kg Mass of the Talk:observable universe